| .file "powl.s" |
| |
| |
| // Copyright (c) 2000 - 2003, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2000 by the Intel Numerics Group, Intel Corporation |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // |
| // * Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in the |
| // documentation and/or other materials provided with the distribution. |
| // |
| // * The name of Intel Corporation may not be used to endorse or promote |
| // products derived from this software without specific prior written |
| // permission. |
| |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
| // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
| // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
| // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Intel Corporation is the author of this code, and requests that all |
| // problem reports or change requests be submitted to it directly at |
| // http://www.intel.com/software/products/opensource/libraries/num.htm. |
| // |
| //********************************************************************* |
| // |
| // Function: powl(x,y), where |
| // y |
| // powl(x,y) = x , for double extended precision x and y values |
| // |
| //********************************************************************* |
| // |
| // History: |
| // 02/02/00 (Hand Optimized) |
| // 04/04/00 Unwind support added |
| // 08/15/00 Bundle added after call to __libm_error_support to properly |
| // set [the previously overwritten] GR_Parameter_RESULT. |
| // 01/22/01 Corrected results for powl(1,inf), powl(1,nan), and |
| // powl(snan,0) to be 1 per C99, not nan. Fixed many flag settings. |
| // 02/06/01 Call __libm_error support if over/underflow when y=2. |
| // 04/17/01 Support added for y close to 1 and x a non-special value. |
| // Shared software under/overflow detection for all paths |
| // 02/07/02 Corrected sf3 setting to disable traps |
| // 05/13/02 Improved performance of all paths |
| // 02/10/03 Reordered header: .section, .global, .proc, .align; |
| // used data8 for long double table values |
| // 04/17/03 Added missing mutex directive |
| // 10/13/03 Corrected .endp names to match .proc names |
| // |
| //********************************************************************* |
| // |
| // Resources Used: |
| // |
| // Floating-Point Registers: |
| // f8 (Input x and Return Value) |
| // f9 (Input y) |
| // f10-f15,f32-f79 |
| // |
| // General Purpose Registers: |
| // Locals r14-24,r32-r65 |
| // Parameters to __libm_error_support r62,r63,r64,r65 |
| // |
| // Predicate Registers: p6-p15 |
| // |
| //********************************************************************* |
| // |
| // Special Cases and IEEE special conditions: |
| // |
| // Denormal fault raised on denormal inputs |
| // Overflow exceptions raised when appropriate for pow |
| // Underflow exceptions raised when appropriate for pow |
| // (Error Handling Routine called for overflow and Underflow) |
| // Inexact raised when appropriate by algorithm |
| // |
| // 1. (anything) ** NatVal or (NatVal) ** anything is NatVal |
| // 2. X or Y unsupported or sNaN is qNaN/Invalid |
| // 3. (anything) ** 0 is 1 |
| // 4. (anything) ** 1 is itself |
| // 5. (anything except 1) ** qNAN is qNAN |
| // 6. qNAN ** (anything except 0) is qNAN |
| // 7. +-(|x| > 1) ** +INF is +INF |
| // 8. +-(|x| > 1) ** -INF is +0 |
| // 9. +-(|x| < 1) ** +INF is +0 |
| // 10. +-(|x| < 1) ** -INF is +INF |
| // 11. +-1 ** +-INF is +1 |
| // 12. +0 ** (+anything except 0, NAN) is +0 |
| // 13. -0 ** (+anything except 0, NAN, odd integer) is +0 |
| // 14. +0 ** (-anything except 0, NAN) is +INF/div_0 |
| // 15. -0 ** (-anything except 0, NAN, odd integer) is +INF/div_0 |
| // 16. -0 ** (odd integer) = -( +0 ** (odd integer) ) |
| // 17. +INF ** (+anything except 0,NAN) is +INF |
| // 18. +INF ** (-anything except 0,NAN) is +0 |
| // 19. -INF ** (anything except NAN) = -0 ** (-anything) |
| // 20. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) |
| // 21. (-anything except 0 and inf) ** (non-integer) is qNAN/Invalid |
| // 22. X or Y denorm/unorm and denorm/unorm operand trap is enabled, |
| // generate denorm/unorm fault except if invalid or div_0 raised. |
| // |
| //********************************************************************* |
| // |
| // Algorithm |
| // ========= |
| // |
| // Special Cases |
| // |
| // If Y = 2, return X*X. |
| // If Y = 0.5, return sqrt(X). |
| // |
| // Compute log(X) to extra precision. |
| // |
| // ker_log_80( X, logX_hi, logX_lo, Safe ); |
| // |
| // ...logX_hi + logX_lo approximates log(X) to roughly 80 |
| // ...significant bits of accuracy. |
| // |
| // Compute Y*log(X) to extra precision. |
| // |
| // P_hi := Y * logX_hi |
| // P_lo := Y * logX_hi - P_hi ...using FMA |
| // P_lo := Y * logX_lo + P_lo ...using FMA |
| // |
| // Compute exp(P_hi + P_lo) |
| // |
| // Flag := 2; |
| // Expo_Range := 2; (assuming double-extended power function) |
| // ker_exp_64( P_hi, P_lo, Flag, Expo_Range, |
| // Z_hi, Z_lo, scale, Safe ) |
| // |
| // scale := sgn * scale |
| // |
| // If (Safe) then ...result will not over/underflow |
| // return scale*Z_hi + (scale*Z_lo) |
| // quickly |
| // Else |
| // take necessary precaution in computing |
| // scale*Z_hi + (scale*Z_lo) |
| // to set possible exceptions correctly. |
| // End If |
| // |
| // Case_Y_Special |
| // |
| // ...Follow the order of the case checks |
| // |
| // If Y is +-0, return +1 without raising any exception. |
| // If Y is +1, return X without raising any exception. |
| // If Y is qNaN, return Y without exception. |
| // If X is qNaN, return X without exception. |
| // |
| // At this point, X is real and Y is +-inf. |
| // Thus |X| can only be 1, strictly bigger than 1, or |
| // strictly less than 1. |
| // |
| // If |X| < 1, then |
| // return ( Y == +inf? +0 : +inf ) |
| // elseif |X| > 1, then |
| // return ( Y == +inf? +0 : +inf ) |
| // else |
| // goto Case_Invalid |
| // |
| // Case_X_Special |
| // |
| // ...Follow the order of the case checks |
| // ...Note that Y is real, finite, non-zero, and not +1. |
| // |
| // If X is qNaN, return X without exception. |
| // |
| // If X is +-0, |
| // return ( Y > 0 ? +0 : +inf ) |
| // |
| // If X is +inf |
| // return ( Y > 0 ? +inf : +0 ) |
| // |
| // If X is -inf |
| // return -0 ** -Y |
| // return ( Y > 0 ? +inf : +0 ) |
| // |
| // Case_Invalid |
| // |
| // Return 0 * inf to generate a quiet NaN together |
| // with an invalid exception. |
| // |
| // Implementation |
| // ============== |
| // |
| // We describe the quick branch since this part is important |
| // in reaching the normal case efficiently. |
| // |
| // STAGE 1 |
| // ------- |
| // This stage contains two threads. |
| // |
| // Stage1.Thread1 |
| // |
| // fclass.m X_excep, X_ok = X, (NatVal or s/qNaN) or |
| // +-0, +-infinity |
| // |
| // fclass.nm X_unsupp, X_supp = X, (NatVal or s/qNaN) or |
| // +-(0, unnorm, norm, infinity) |
| // |
| // X_norm := fnorm( X ) with traps disabled |
| // |
| // If (X_excep) goto Filtering (Step 2) |
| // If (X_unsupp) goto Filtering (Step 2) |
| // |
| // Stage1.Thread2 |
| // .............. |
| // |
| // fclass.m Y_excep, Y_ok = Y, (NatVal or s/qNaN) or |
| // +-0, +-infinity |
| // |
| // fclass.nm Y_unsupp, Y_supp = Y, (NatVal or s/qNaN) or |
| // +-(0, unnorm, norm, infinity) |
| // |
| // Y_norm := fnorm( Y ) with traps disabled |
| // |
| // If (Y_excep) goto Filtering (Step 2) |
| // If (Y_unsupp) goto Filtering (Step 2) |
| // |
| // |
| // STAGE 2 |
| // ------- |
| // This stage contains two threads. |
| // |
| // Stage2.Thread1 |
| // .............. |
| // |
| // Set X_lt_0 if X < 0 (using fcmp) |
| // sgn := +1.0 |
| // If (X_lt_0) goto Filtering (Step 2) |
| // |
| // Stage2.Thread2 |
| // .............. |
| // |
| // Set Y_is_1 if Y = +1 (using fcmp) |
| // If (Y_is_1) goto Filtering (Step 2) |
| // |
| // STAGE 3 |
| // ------- |
| // This stage contains two threads. |
| // |
| // |
| // Stage3.Thread1 |
| // .............. |
| // |
| // X := fnorm(X) in prevailing traps |
| // |
| // |
| // Stage3.Thread2 |
| // .............. |
| // |
| // Y := fnorm(Y) in prevailing traps |
| // |
| // STAGE 4 |
| // ------- |
| // |
| // Go to Case_Normal. |
| // |
| |
| |
| // ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** |
| |
| // double-extended 1/ln(2) |
| // 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88 |
| // 3fff b8aa 3b29 5c17 f0bc |
| // For speed the significand will be loaded directly with a movl and setf.sig |
| // and the exponent will be bias+63 instead of bias+0. Thus subsequent |
| // computations need to scale appropriately. |
| // The constant 2^12/ln(2) is needed for the computation of N. This is also |
| // obtained by scaling the computations. |
| // |
| // Two shifting constants are loaded directly with movl and setf.d. |
| // 1. RSHF_2TO51 = 1.1000..00 * 2^(63-12) |
| // This constant is added to x*1/ln2 to shift the integer part of |
| // x*2^12/ln2 into the rightmost bits of the significand. |
| // The result of this fma is N_signif. |
| // 2. RSHF = 1.1000..00 * 2^(63) |
| // This constant is subtracted from N_signif * 2^(-51) to give |
| // the integer part of N, N_fix, as a floating-point number. |
| // The result of this fms is float_N. |
| RODATA |
| |
| .align 16 |
| // L_hi, L_lo |
| LOCAL_OBJECT_START(Constants_exp_64_Arg) |
| data8 0xB17217F400000000,0x00003FF2 // L_hi = hi part log(2)/2^12 |
| data8 0xF473DE6AF278ECE6,0x00003FD4 // L_lo = lo part log(2)/2^12 |
| LOCAL_OBJECT_END(Constants_exp_64_Arg) |
| |
| LOCAL_OBJECT_START(Constants_exp_64_A) |
| // Reversed |
| data8 0xAAAAAAABB1B736A0,0x00003FFA |
| data8 0xAAAAAAAB90CD6327,0x00003FFC |
| data8 0xFFFFFFFFFFFFFFFF,0x00003FFD |
| LOCAL_OBJECT_END(Constants_exp_64_A) |
| |
| LOCAL_OBJECT_START(Constants_exp_64_P) |
| // Reversed |
| data8 0xD00D6C8143914A8A,0x00003FF2 |
| data8 0xB60BC4AC30304B30,0x00003FF5 |
| data8 0x888888887474C518,0x00003FF8 |
| data8 0xAAAAAAAA8DAE729D,0x00003FFA |
| data8 0xAAAAAAAAAAAAAF61,0x00003FFC |
| data8 0x80000000000004C7,0x00003FFE |
| LOCAL_OBJECT_END(Constants_exp_64_P) |
| |
| LOCAL_OBJECT_START(Constants_exp_64_T1) |
| data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 |
| data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 |
| data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC |
| data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D |
| data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA |
| data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516 |
| data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A |
| data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4 |
| data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B |
| data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD |
| data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15 |
| data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B |
| data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5 |
| data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A |
| data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177 |
| data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C |
| LOCAL_OBJECT_END(Constants_exp_64_T1) |
| |
| LOCAL_OBJECT_START(Constants_exp_64_T2) |
| data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 |
| data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 |
| data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E |
| data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 |
| data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 |
| data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA |
| data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 |
| data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A |
| data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 |
| data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA |
| data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 |
| data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA |
| data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 |
| data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 |
| data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE |
| data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37 |
| LOCAL_OBJECT_END(Constants_exp_64_T2) |
| |
| LOCAL_OBJECT_START(Constants_exp_64_W1) |
| data8 0x0000000000000000, 0xBE384454171EC4B4 |
| data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8 |
| data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36 |
| data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE |
| data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F |
| data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329 |
| data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5 |
| data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F |
| data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF |
| data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F |
| data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92 |
| data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E |
| data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D |
| data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29 |
| data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A |
| data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA |
| data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6 |
| data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF |
| data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC |
| data8 0xBE51C2141AA42614, 0xBE48D087C37293F4 |
| data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38 |
| data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962 |
| data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788 |
| data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7 |
| data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2 |
| data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4 |
| data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA |
| data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B |
| data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A |
| data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719 |
| data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D |
| data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707 |
| LOCAL_OBJECT_END(Constants_exp_64_W1) |
| |
| LOCAL_OBJECT_START(Constants_exp_64_W2) |
| data8 0x0000000000000000, 0xBE641F2537A3D7A2 |
| data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6 |
| data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE |
| data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3 |
| data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4 |
| data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B |
| data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7 |
| data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA |
| data8 0xBE56856B49BFF529, 0x3E66DD3300508651 |
| data8 0x3E51165FC114BC13, 0x3E53333DC453290F |
| data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696 |
| data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93 |
| data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE |
| data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22 |
| data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97 |
| data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8 |
| data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC |
| data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1 |
| data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7 |
| data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D |
| data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C |
| data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5 |
| data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9 |
| data8 0xBE559725ADE45917, 0xBE68C29C042FC476 |
| data8 0xBE67593B01E511FA, 0xBE4A4313398801ED |
| data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E |
| data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D |
| data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F |
| data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1 |
| data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795 |
| data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E |
| data8 0x3E68BF5C17365712, 0x3E3956F9B3785569 |
| LOCAL_OBJECT_END(Constants_exp_64_W2) |
| |
| LOCAL_OBJECT_START(Constants_log_80_P) |
| // P_8, P_7, ..., P_1 |
| data8 0xCCCE8B883B1042BC, 0x0000BFFB // P_8 |
| data8 0xE38997B7CADC2149, 0x00003FFB // P_7 |
| data8 0xFFFFFFFEB1ACB090, 0x0000BFFB // P_6 |
| data8 0x9249249806481C81, 0x00003FFC // P_5 |
| data8 0x0000000000000000, 0x00000000 // Pad for bank conflicts |
| data8 0xAAAAAAAAAAAAB0EF, 0x0000BFFC // P_4 |
| data8 0xCCCCCCCCCCC91416, 0x00003FFC // P_3 |
| data8 0x8000000000000000, 0x0000BFFD // P_2 |
| data8 0xAAAAAAAAAAAAAAAB, 0x00003FFD // P_1 |
| LOCAL_OBJECT_END(Constants_log_80_P) |
| |
| LOCAL_OBJECT_START(Constants_log_80_Q) |
| // log2_hi, log2_lo, Q_6, Q_5, Q_4, Q_3, Q_2, Q_1 |
| data8 0xB172180000000000,0x00003FFE |
| data8 0x82E308654361C4C6,0x0000BFE2 |
| data8 0x92492453A51BE0AF,0x00003FFC |
| data8 0xAAAAAB73A0CFD29F,0x0000BFFC |
| data8 0xCCCCCCCCCCCE3872,0x00003FFC |
| data8 0xFFFFFFFFFFFFB4FB,0x0000BFFC |
| data8 0xAAAAAAAAAAAAAAAB,0x00003FFD |
| data8 0x8000000000000000,0x0000BFFE |
| LOCAL_OBJECT_END(Constants_log_80_Q) |
| |
| LOCAL_OBJECT_START(Constants_log_80_Z_G_H_h1) |
| // Z1 - 16 bit fixed, G1 and H1 IEEE single, h1 IEEE double |
| data4 0x00008000,0x3F800000,0x00000000,0x00000000 |
| data4 0x00000000,0x00000000,0x00000000,0x00000000 |
| data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000 |
| data4 0xEBA0E0D1,0x8B1D330B,0x00003FDA,0x00000000 |
| data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000 |
| data4 0x9EADD553,0xE2AF365E,0x00003FE2,0x00000000 |
| data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000 |
| data4 0x752F34A2,0xF585FEC3,0x0000BFE3,0x00000000 |
| data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000 |
| data4 0x893B03F3,0xF3546435,0x00003FE2,0x00000000 |
| data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000 |
| data4 0x39CDD2AC,0xBABA62E0,0x00003FE4,0x00000000 |
| data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000 |
| data4 0x457978A1,0x8718789F,0x00003FE2,0x00000000 |
| data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000 |
| data4 0x3185E56A,0x9442DF96,0x0000BFE4,0x00000000 |
| data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000 |
| data4 0x2BBE2CBD,0xCBF9A4BF,0x00003FE4,0x00000000 |
| data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000 |
| data4 0x852D5935,0xF3537535,0x00003FE3,0x00000000 |
| data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000 |
| data4 0x46CDF32F,0xA1F1E699,0x0000BFDF,0x00000000 |
| data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000 |
| data4 0xD8484CE3,0x84A61856,0x00003FE4,0x00000000 |
| data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000 |
| data4 0xFF28821B,0xC7DD97E0,0x0000BFE2,0x00000000 |
| data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000 |
| data4 0xEF1FD32F,0xD3C4A887,0x00003FE3,0x00000000 |
| data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000 |
| data4 0x464C76DA,0x84672BE6,0x00003FE5,0x00000000 |
| data4 0x00004211,0x3F042108,0x3F29516A,0x00000000 |
| data4 0x18835FB9,0x9A43A511,0x0000BFE5,0x00000000 |
| LOCAL_OBJECT_END(Constants_log_80_Z_G_H_h1) |
| |
| LOCAL_OBJECT_START(Constants_log_80_Z_G_H_h2) |
| // Z2 - 16 bit fixed, G2 and H2 IEEE single, h2 IEEE double |
| data4 0x00008000,0x3F800000,0x00000000,0x00000000 |
| data4 0x00000000,0x00000000,0x00000000,0x00000000 |
| data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000 |
| data4 0x211398BF,0xAD08B116,0x00003FDB,0x00000000 |
| data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000 |
| data4 0xC376958E,0xB106790F,0x00003FDE,0x00000000 |
| data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000 |
| data4 0x79A7679A,0xFD03F242,0x0000BFDA,0x00000000 |
| data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000 |
| data4 0x05E7AE08,0xF03F81C3,0x0000BFDF,0x00000000 |
| data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000 |
| data4 0x049EB22F,0xD1B87D3C,0x00003FDE,0x00000000 |
| data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000 |
| data4 0x3A9E81E0,0xFABC8B95,0x00003FDF,0x00000000 |
| data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000 |
| data4 0x7C4B5443,0xF5F3653F,0x00003FDF,0x00000000 |
| data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000 |
| data4 0xF65A1773,0xE78AB204,0x00003FE0,0x00000000 |
| data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000 |
| data4 0x7B8EF695,0xDB7CBFFF,0x0000BFE0,0x00000000 |
| data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000 |
| data4 0xCF773FB3,0xC0241AEA,0x0000BFE0,0x00000000 |
| data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000 |
| data4 0xC9539FDF,0xFC8F4D48,0x00003FE1,0x00000000 |
| data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000 |
| data4 0x954665C2,0x9CD035FB,0x0000BFE1,0x00000000 |
| data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000 |
| data4 0xDD367A30,0xEC9017C7,0x00003FE1,0x00000000 |
| data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000 |
| data4 0xCB11189C,0xEE6625D3,0x0000BFE1,0x00000000 |
| data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000 |
| data4 0xBE11C424,0xA49C8DB5,0x0000BFE0,0x00000000 |
| LOCAL_OBJECT_END(Constants_log_80_Z_G_H_h2) |
| |
| LOCAL_OBJECT_START(Constants_log_80_h3_G_H) |
| // h3 IEEE double extended, H3 and G3 IEEE single |
| data4 0x112666B0,0xAAACAAB1,0x00003FD3,0x3F7FFC00 |
| data4 0x9B7FAD21,0x90051030,0x00003FD8,0x3F7FF400 |
| data4 0xF4D783C4,0xA6B46F46,0x00003FDA,0x3F7FEC00 |
| data4 0x11C6DDCA,0xDA148D88,0x0000BFD8,0x3F7FE400 |
| data4 0xCA964D95,0xCE65C1D8,0x0000BFD8,0x3F7FDC00 |
| data4 0x23412D13,0x883838EE,0x0000BFDB,0x3F7FD400 |
| data4 0x983ED687,0xB7E5CFA1,0x00003FDB,0x3F7FCC08 |
| data4 0xE3C3930B,0xDBE23B16,0x0000BFD9,0x3F7FC408 |
| data4 0x48AA4DFC,0x9B92F1FC,0x0000BFDC,0x3F7FBC10 |
| data4 0xCE9C8F7E,0x9A8CEB15,0x0000BFD9,0x3F7FB410 |
| data4 0x0DECE74A,0x8C220879,0x00003FDC,0x3F7FAC18 |
| data4 0x2F053150,0xB25CA912,0x0000BFDA,0x3F7FA420 |
| data4 0xD9A5BE20,0xA5876555,0x00003FDB,0x3F7F9C20 |
| data4 0x2053F087,0xC919BB6E,0x00003FD9,0x3F7F9428 |
| data4 0x041E9A77,0xB70BDA79,0x00003FDC,0x3F7F8C30 |
| data4 0xEA1C9C30,0xF18A5C08,0x00003FDA,0x3F7F8438 |
| data4 0x796D89E5,0xA3790D84,0x0000BFDD,0x3F7F7C40 |
| data4 0xA2915A3A,0xE1852369,0x0000BFDD,0x3F7F7448 |
| data4 0xA39ED868,0xD803858F,0x00003FDC,0x3F7F6C50 |
| data4 0x9417EBB7,0xB2EEE356,0x0000BFDD,0x3F7F6458 |
| data4 0x9BB0D07F,0xED5C1F8A,0x0000BFDC,0x3F7F5C68 |
| data4 0xE87C740A,0xD6D201A0,0x0000BFDD,0x3F7F5470 |
| data4 0x1CA74025,0xE8DEBF5E,0x00003FDC,0x3F7F4C78 |
| data4 0x1F34A7EB,0x9A995A97,0x0000BFDC,0x3F7F4488 |
| data4 0x359EED97,0x9CB0F742,0x0000BFDA,0x3F7F3C90 |
| data4 0xBBC6A1C8,0xD6F833C2,0x0000BFDD,0x3F7F34A0 |
| data4 0xE71090EC,0xE1F68F2A,0x00003FDC,0x3F7F2CA8 |
| data4 0xC160A74F,0xD1881CF1,0x0000BFDB,0x3F7F24B8 |
| data4 0xD78CB5A4,0x9AD05AE2,0x00003FD6,0x3F7F1CC8 |
| data4 0x9A77DC4B,0xE658CB8E,0x0000BFDD,0x3F7F14D8 |
| data4 0x6BD6D312,0xBA281296,0x00003FDC,0x3F7F0CE0 |
| data4 0xF95210D0,0xB478BBEB,0x0000BFDB,0x3F7F04F0 |
| data4 0x38800100,0x39400480,0x39A00640,0x39E00C41 // H's start here |
| data4 0x3A100A21,0x3A300F22,0x3A4FF51C,0x3A6FFC1D |
| data4 0x3A87F20B,0x3A97F68B,0x3AA7EB86,0x3AB7E101 |
| data4 0x3AC7E701,0x3AD7DD7B,0x3AE7D474,0x3AF7CBED |
| data4 0x3B03E1F3,0x3B0BDE2F,0x3B13DAAA,0x3B1BD766 |
| data4 0x3B23CC5C,0x3B2BC997,0x3B33C711,0x3B3BBCC6 |
| data4 0x3B43BAC0,0x3B4BB0F4,0x3B53AF6D,0x3B5BA620 |
| data4 0x3B639D12,0x3B6B9444,0x3B7393BC,0x3B7B8B6D |
| LOCAL_OBJECT_END(Constants_log_80_h3_G_H) |
| |
| GR_sig_inv_ln2 = r14 |
| GR_rshf_2to51 = r15 |
| GR_exp_2tom51 = r16 |
| GR_rshf = r17 |
| GR_exp_half = r18 |
| GR_sign_mask = r19 |
| GR_exp_square_oflow = r20 |
| GR_exp_square_uflow = r21 |
| GR_exp_ynear1_oflow = r22 |
| GR_exp_ynear1_uflow = r23 |
| GR_signif_Z = r24 |
| |
| GR_signexp_x = r32 |
| |
| GR_exp_x = r33 |
| |
| GR_Table_Ptr = r34 |
| |
| GR_Table_Ptr1 = r35 |
| |
| GR_Index1 = r36 |
| |
| GR_Index2 = r37 |
| GR_Expo_X = r37 |
| |
| GR_M = r38 |
| |
| GR_X_0 = r39 |
| GR_Mask = r39 |
| |
| GR_X_1 = r40 |
| GR_W1_ptr = r40 |
| |
| GR_W2_ptr = r41 |
| GR_X_2 = r41 |
| |
| GR_Z_1 = r42 |
| GR_M2 = r42 |
| |
| GR_M1 = r43 |
| GR_Z_2 = r43 |
| |
| GR_N = r44 |
| GR_k = r44 |
| |
| GR_Big_Pos_Exp = r45 |
| |
| GR_exp_pos_max = r46 |
| |
| GR_exp_bias_p_k = r47 |
| |
| GR_Index3 = r48 |
| GR_temp = r48 |
| |
| GR_vsm_expo = r49 |
| |
| GR_T1_ptr = r50 |
| GR_P_ptr1 = r50 |
| GR_T2_ptr = r51 |
| GR_P_ptr2 = r51 |
| GR_N_fix = r52 |
| GR_exp_y = r53 |
| GR_signif_y = r54 |
| GR_signexp_y = r55 |
| GR_fraction_y = r55 |
| GR_low_order_bit = r56 |
| GR_exp_mask = r57 |
| GR_exp_bias = r58 |
| GR_y_sign = r59 |
| GR_table_base = r60 |
| GR_ptr_exp_Arg = r61 |
| GR_Delta_Exp = r62 |
| GR_Special_Exp = r63 |
| GR_exp_neg_max = r64 |
| GR_Big_Neg_Exp = r65 |
| |
| //** Registers for unwind support |
| |
| GR_SAVE_PFS = r59 |
| GR_SAVE_B0 = r60 |
| GR_SAVE_GP = r61 |
| GR_Parameter_X = r62 |
| GR_Parameter_Y = r63 |
| GR_Parameter_RESULT = r64 |
| GR_Parameter_TAG = r65 |
| |
| //** |
| |
| FR_Input_X = f8 |
| FR_Result = f8 |
| FR_Input_Y = f9 |
| |
| FR_Neg = f10 |
| FR_P_hi = f10 |
| FR_X = f10 |
| |
| FR_Half = f11 |
| FR_h_3 = f11 |
| FR_poly_hi = f11 |
| |
| FR_Sgn = f12 |
| |
| FR_half_W = f13 |
| |
| FR_X_cor = f14 |
| FR_P_lo = f14 |
| |
| FR_W = f15 |
| |
| FR_X_lo = f32 |
| |
| FR_S = f33 |
| FR_W3 = f33 |
| |
| FR_Y_hi = f34 |
| FR_logx_hi = f34 |
| |
| FR_Z = f35 |
| FR_logx_lo = f35 |
| FR_GS_hi = f35 |
| FR_Y_lo = f35 |
| |
| FR_r_cor = f36 |
| FR_Scale = f36 |
| |
| FR_G_1 = f37 |
| FR_G = f37 |
| FR_Wsq = f37 |
| FR_temp = f37 |
| |
| FR_H_1 = f38 |
| FR_H = f38 |
| FR_W4 = f38 |
| |
| FR_h = f39 |
| FR_h_1 = f39 |
| FR_N = f39 |
| FR_P_7 = f39 |
| |
| FR_G_2 = f40 |
| FR_P_8 = f40 |
| FR_L_hi = f40 |
| |
| FR_H_2 = f41 |
| FR_L_lo = f41 |
| FR_A_1 = f41 |
| |
| FR_h_2 = f42 |
| |
| FR_W1 = f43 |
| |
| FR_G_3 = f44 |
| FR_P_8 = f44 |
| FR_T1 = f44 |
| |
| FR_log2_hi = f45 |
| FR_W2 = f45 |
| |
| FR_GS_lo = f46 |
| FR_T2 = f46 |
| |
| FR_W_1_p1 = f47 |
| FR_H_3 = f47 |
| |
| FR_float_N = f48 |
| |
| FR_A_2 = f49 |
| |
| FR_Q_4 = f50 |
| FR_r4 = f50 |
| |
| FR_Q_3 = f51 |
| FR_A_3 = f51 |
| |
| FR_Q_2 = f52 |
| FR_P_2 = f52 |
| |
| FR_Q_1 = f53 |
| FR_P_1 = f53 |
| FR_T = f53 |
| |
| FR_Wp1 = f54 |
| FR_Q_5 = f54 |
| FR_P_3 = f54 |
| |
| FR_Q_6 = f55 |
| |
| FR_log2_lo = f56 |
| FR_Two = f56 |
| |
| FR_Big = f57 |
| |
| FR_neg_2_mK = f58 |
| |
| FR_r = f59 |
| |
| FR_poly_lo = f60 |
| |
| FR_poly = f61 |
| |
| FR_P_5 = f62 |
| FR_Result_small = f62 |
| |
| FR_rsq = f63 |
| |
| FR_Delta = f64 |
| |
| FR_save_Input_X = f65 |
| FR_norm_X = f66 |
| FR_norm_Y = f67 |
| FR_Y_lo_2 = f68 |
| |
| FR_P_6 = f69 |
| FR_Result_big = f69 |
| |
| FR_RSHF_2TO51 = f70 |
| FR_INV_LN2_2TO63 = f71 |
| FR_2TOM51 = f72 |
| FR_RSHF = f73 |
| FR_TMP1 = f74 |
| FR_TMP2 = f75 |
| FR_TMP3 = f76 |
| FR_Tscale = f77 |
| FR_P_4 = f78 |
| FR_NBig = f79 |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(powl) |
| // |
| // Get significand of x. It is the critical path. |
| // |
| { .mfi |
| getf.sig GR_signif_Z = FR_Input_X // Get significand of x |
| fclass.m p11, p12 = FR_Input_X, 0x0b // Test x unorm |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fnorm.s1 FR_norm_X = FR_Input_X // Normalize x |
| mov GR_exp_half = 0xffff - 1 // Exponent for 0.5 |
| } |
| ;; |
| |
| { .mfi |
| alloc r32 = ar.pfs,0,30,4,0 |
| fclass.m p7, p0 = FR_Input_Y, 0x1E7 // Test y natval, nan, inf, zero |
| mov GR_exp_pos_max = 0x13fff // Max exponent for pos oflow test |
| } |
| { .mfi |
| addl GR_table_base = @ltoff(Constants_exp_64_Arg#), gp // Ptr to tables |
| fnorm.s1 FR_norm_Y = FR_Input_Y // Normalize y |
| mov GR_exp_neg_max = 0x33fff // Max exponent for neg oflow test |
| } |
| ;; |
| |
| { .mfi |
| getf.exp GR_signexp_y = FR_Input_Y // Get sign and exp of y |
| (p12) fclass.m p11, p0 = FR_Input_Y, 0x0b // Test y unorm |
| mov GR_sign_mask = 0x20000 // Sign mask |
| } |
| { .mfi |
| ld8 GR_table_base = [GR_table_base] // Get base address for tables |
| fadd.s1 FR_Two = f1, f1 // Form 2.0 for square test |
| mov GR_exp_mask = 0x1FFFF // Exponent mask |
| } |
| ;; |
| |
| { .mfi |
| getf.sig GR_signif_y = FR_Input_Y // Get significand of y |
| fclass.m p6, p0 = FR_Input_X, 0x1E7 // Test x natval, nan, inf, zero |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| getf.exp GR_signexp_x = FR_Input_X // Get signexp of x |
| fmerge.s FR_save_Input_X = FR_Input_X, FR_Input_X |
| extr.u GR_Index1 = GR_signif_Z, 59, 4 // Extract upper 4 signif bits of x |
| } |
| { .mfb |
| setf.exp FR_Half = GR_exp_half // Load half |
| nop.f 999 |
| (p11) br.cond.spnt POWL_DENORM // Branch if x or y denorm/unorm |
| } |
| ;; |
| |
| // Return here from POWL_DENORM |
| POWL_COMMON: |
| { .mfi |
| setf.exp FR_Big = GR_exp_pos_max // Form big pos value for oflow test |
| fclass.nm p11, p0 = FR_Input_Y, 0x1FF // Test Y unsupported |
| shl GR_Index1 = GR_Index1,5 // Adjust index1 pointer x 32 |
| } |
| { .mfi |
| add GR_Table_Ptr = 0x7c0, GR_table_base // Constants_log_80_Z_G_H_h1 |
| fma.s1 FR_Sgn = f1,f1,f0 // Assume result positive |
| mov GR_exp_bias = 0xFFFF // Form exponent bias |
| } |
| ;; |
| |
| // |
| // Identify NatVals, NaNs, Infs, and Zeros. |
| // |
| // |
| // Remove sign bit from exponent of y. |
| // Check for x = 1 |
| // Branch on Infs, Nans, Zeros, and Natvals |
| // Check to see that exponent < 0 |
| // |
| { .mfi |
| setf.exp FR_NBig = GR_exp_neg_max // Form big neg value for oflow test |
| fclass.nm p8, p0 = FR_Input_X, 0x1FF // Test X unsupported |
| and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent of y |
| } |
| { .mfb |
| add GR_Index1 = GR_Index1,GR_Table_Ptr |
| nop.f 999 |
| (p6) br.cond.spnt POWL_64_SPECIAL // Branch if x natval, nan, inf, zero |
| } |
| ;; |
| |
| // load Z_1 from Index1 |
| |
| // There is logic starting here to determine if y is an integer when x < 0. |
| // If 0 < |y| < 1 then clearly y is not an integer. |
| // If |y| > 1, then the significand of y is shifted left by the size of |
| // the exponent of y. This preserves the lsb of the integer part + the |
| // fractional bits. The lsb of the integer can be tested to determine if |
| // the integer is even or odd. The fractional bits can be tested. If zero, |
| // then y is an integer. |
| // |
| { .mfi |
| ld2 GR_Z_1 =[GR_Index1],4 // Load Z_1 |
| fmerge.s FR_Z = f0, FR_norm_X // Z = |x| |
| extr.u GR_X_0 = GR_signif_Z, 49, 15 // Extract X_0 from significand |
| } |
| { .mfb |
| cmp.lt p9, p0 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 |
| nop.f 999 |
| (p7) br.cond.spnt POWL_64_SPECIAL // Branch if y natval, nan, inf, zero |
| } |
| ;; |
| |
| { .mfb |
| ldfs FR_G_1 = [GR_Index1],4 // Load G_1 |
| fcmp.eq.s1 p10, p0 = FR_Input_Y, f1 // Test Y = +1.0 |
| (p8) br.cond.spnt POWL_64_UNSUPPORT // Branch if x unsupported |
| } |
| ;; |
| |
| // |
| // X_0 = High order 15 bit of Z |
| // |
| { .mfb |
| ldfs FR_H_1 = [GR_Index1],8 // Load H_1 |
| (p9) fcmp.lt.unc.s1 p9, p0 = FR_Input_X, f0 // Test x<0, 0 <|y|<1 |
| (p11) br.cond.spnt POWL_64_UNSUPPORT // Branch if y unsupported |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_h_1 = [GR_Index1] // Load h_1 |
| fcmp.eq.s1 p7, p0 = FR_Input_Y, FR_Two // Test y = 2.0 |
| pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // X_1 = X_0 * Z_1 (bits 15-30) |
| // Wait 4 cycles to use result |
| } |
| { .mfi |
| add GR_Table_Ptr = 0x9c0, GR_table_base // Constants_log_80_Z_G_H_h2 |
| nop.f 999 |
| sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent of y |
| } |
| ;; |
| |
| // |
| // Branch for (x < 0) and Y not an integer. |
| // |
| { .mfb |
| nop.m 999 |
| fcmp.lt.s1 p6, p0 = FR_Input_X, f0 // Test x < 0 |
| (p9) br.cond.spnt POWL_64_XNEG // Branch if x < 0, 0 < |y| < 1 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s1 p12, p0 = FR_Input_X, f1 // Test x=+1.0 |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| fsub.s1 FR_W = FR_Z, f1 // W = Z - 1 |
| (p7) br.cond.spnt POWL_64_SQUARE // Branch if y=2 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p10) fmpy.s0 FR_Result = FR_Input_X, f1 // If y=+1.0, result=x |
| (p6) shl GR_fraction_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction |
| // Wait 4 cycles to use result |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p12) fma.s0 FR_Result = FR_Input_Y, f0, f1 // If x=1.0, result=1, chk denorm |
| extr.u GR_Index2 = GR_X_1, 6, 4 // Extract index2 |
| } |
| ;; |
| |
| // |
| // N = exponent of Z |
| // |
| { .mib |
| getf.exp GR_N = FR_Z // Get exponent of Z (also x) |
| shl GR_Index2=GR_Index2,5 // Index2 x 32 bytes |
| (p10) br.ret.spnt b0 // Exit if y=+1.0 |
| } |
| ;; |
| |
| { .mib |
| add GR_Index2 = GR_Index2, GR_Table_Ptr // Pointer to table 2 |
| nop.i 999 |
| (p12) br.ret.spnt b0 // Exit if x=+1.0 |
| } |
| ;; |
| |
| { .mmi |
| ld2 GR_Z_2 =[GR_Index2],4 // Load Z_2 |
| ;; |
| ldfs FR_G_2 = [GR_Index2],4 // Load G_2 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mii |
| ldfs FR_H_2 = [GR_Index2],8 // Load H_2 |
| (p6) tbit.nz.unc p9, p0 = GR_fraction_y, 63 // Test x<0 and y odd integer |
| add GR_Table_Ptr = 0xbcc, GR_table_base // Constants_log_80_h3_G_H, G_3 |
| } |
| ;; |
| |
| // |
| // For x < 0 and y odd integer,, set sign = -1. |
| // |
| { .mfi |
| getf.exp GR_M = FR_W // Get signexp of W |
| nop.f 999 |
| pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // X_2 = X_1 * Z_2 (bits 15-30) |
| } |
| { .mfi |
| ldfe FR_h_2 = [GR_Index2] // Load h_2 |
| (p9) fnma.s1 FR_Sgn = f1, f1, f0 // If x<0, y odd int, result negative |
| sub GR_N = GR_N, GR_exp_bias // Get true exponent of x = N |
| } |
| ;; |
| |
| { .mfi |
| add GR_Table_Ptr1 = 0xdc0, GR_table_base // Ptr to H_3 |
| fcmp.eq.s0 p11, p0 = FR_Input_Y, FR_Half // Test y=0.5, also set denorm |
| (p6) shl GR_fraction_y= GR_fraction_y, 1 // Shift left 1 to get fraction |
| } |
| ;; |
| |
| { .mmb |
| setf.sig FR_float_N = GR_N |
| (p6) cmp.ne.unc p8, p0 = GR_fraction_y, r0 // Test x<0 and y not integer |
| (p8) br.cond.spnt POWL_64_XNEG // Branch if x<0 and y not int |
| } |
| ;; |
| |
| // |
| // Raise possible denormal operand exception for both X and Y. |
| // Set pointers in case |x| near 1 |
| // Branch to embedded sqrt(x) if y=0.5 |
| // |
| { .mfi |
| add GR_P_ptr1 = 0x6b0, GR_table_base // Constants_log_80_P, P8, NEAR path |
| fcmp.eq.s0 p12, p0 = FR_Input_X, FR_Input_Y // Dummy to set denormal |
| add GR_P_ptr2 = 0x700, GR_table_base // Constants_log_80_P, P4, NEAR path |
| } |
| { .mfb |
| cmp.eq p15, p14 = r0, r0 // Assume result safe (no over/under) |
| fsub.s1 FR_Delta = FR_Input_Y,f1 // Delta = y - 1.0 |
| (p11) br.cond.spnt POWL_64_SQRT // Branch if y=0.5 |
| } |
| ;; |
| |
| // |
| // Computes ln( x ) to extra precision |
| // Input FR 1: FR_X |
| // Output FR 2: FR_Y_hi |
| // Output FR 3: FR_Y_lo |
| // Output PR 1: PR_Safe |
| // |
| { .mfi |
| and GR_M = GR_exp_mask, GR_M // Mask to get exponent of W |
| nop.f 999 |
| extr.u GR_Index3 = GR_X_2, 1, 5 // Get index3 |
| } |
| ;; |
| |
| { .mmi |
| shladd GR_Table_Ptr1 = GR_Index3,2,GR_Table_Ptr1 // Ptr to H_3 |
| shladd GR_Index3 = GR_Index3,4,GR_Table_Ptr // Ptr to G_3 |
| sub GR_M = GR_M, GR_exp_bias // Get true exponent of W |
| } |
| ;; |
| |
| { .mib |
| ldfs FR_G_3 = [GR_Index3],-12 // Load G_3 |
| cmp.gt p7, p14 = -8, GR_M // Test if |x-1| < 2^-8 |
| (p7) br.cond.spnt LOGL80_NEAR // Branch if |x-1| < 2^-8 |
| } |
| ;; |
| |
| // Here if |x-1| >= 2^-8 |
| { .mmf |
| ldfs FR_H_3 = [GR_Table_Ptr1] // Load H_3 |
| nop.m 999 |
| nop.f 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_h_3 = [GR_Index3] // Load h_3 |
| fmerge.se FR_S = f1,FR_Z // S = merge of 1.0 and signif(Z) |
| nop.i 999 |
| } |
| { .mfi |
| add GR_Table_Ptr = 0x740, GR_table_base // Constants_log_80_Q |
| fmpy.s1 FR_G = FR_G_1, FR_G_2 // G = G_1 * G_2 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Begin Loading Q's - load log2_hi part |
| // |
| { .mfi |
| ldfe FR_log2_hi = [GR_Table_Ptr],16 // Load log2_hi |
| fadd.s1 FR_H = FR_H_1, FR_H_2 // H = H_1 + H_2 |
| nop.i 999 |
| };; |
| |
| // |
| // h = h_1 + h_2 |
| // |
| { .mfi |
| ldfe FR_log2_lo = [GR_Table_Ptr],16 // Load log2_lo |
| fadd.s1 FR_h = FR_h_1, FR_h_2 // h = h_1 + h_2 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_Q_6 = [GR_Table_Ptr],16 // Load Q_6 |
| fcvt.xf FR_float_N = FR_float_N |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_Q_5 = [GR_Table_Ptr],16 // Load Q_5 |
| nop.f 999 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // G = G_1 * G_2 * G_3 |
| // |
| { .mfi |
| ldfe FR_Q_4 = [GR_Table_Ptr],16 // Load Q_4 |
| fmpy.s1 FR_G = FR_G, FR_G_3 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // H = H_1 + H_2 + H_3 |
| // |
| { .mfi |
| ldfe FR_Q_3 = [GR_Table_Ptr],16 // Load Q_3 |
| fadd.s1 FR_H = FR_H, FR_H_3 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Y_lo = poly + Y_lo |
| // |
| // h = h_1 + h_2 + h_3 |
| // |
| { .mfi |
| ldfe FR_Q_2 = [GR_Table_Ptr],16 // Load Q_2 |
| fadd.s1 FR_h = FR_h, FR_h_3 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // GS_hi = G*S |
| // r = G*S -1 |
| // |
| { .mfi |
| ldfe FR_Q_1 = [GR_Table_Ptr],16 // Load Q_1 |
| fmpy.s1 FR_GS_hi = FR_G, FR_S |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fms.s1 FR_r = FR_G, FR_S, f1 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // poly_lo = Q_5 + r * Q_6 |
| // |
| { .mfi |
| getf.exp GR_Delta_Exp = FR_Delta // Get signexp of y-1 for exp calc |
| fma.s1 FR_poly_lo = FR_r, FR_Q_6, FR_Q_5 |
| nop.i 999 |
| } |
| // |
| // r_cor = GS_hi -1 |
| // |
| { .mfi |
| nop.m 999 |
| fsub.s1 FR_r_cor = FR_GS_hi, f1 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // GS_lo = G*S - GS_hi |
| // |
| { .mfi |
| nop.m 999 |
| fms.s1 FR_GS_lo = FR_G, FR_S, FR_GS_hi |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // rsq = r * r |
| // |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_rsq = FR_r, FR_r |
| nop.i 999 |
| } |
| // |
| // G = float_N*log2_hi + H |
| // |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_G = FR_float_N, FR_log2_hi, FR_H |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Y_lo = float_N*log2_lo + h |
| // |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_Y_lo = FR_float_N, FR_log2_lo, FR_h |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // poly_lo = Q_4 + r * poly_lo |
| // r_cor = r_cor - r |
| // |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_4 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fsub.s1 FR_r_cor = FR_r_cor, FR_r |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // poly_hi = r * Q_2 + Q_1 |
| // Y_hi = G + r |
| // |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_r, FR_Q_2, FR_Q_1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fadd.s1 FR_Y_hi = FR_G, FR_r |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // poly_lo = Q_3 + r * poly_lo |
| // r_cor = r_cor + GS_lo |
| // |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_lo = FR_r, FR_poly_lo, FR_Q_3 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fadd.s1 FR_r_cor = FR_r_cor, FR_GS_lo |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Y_lo = G - Y_hi |
| // |
| { .mfi |
| nop.m 999 |
| fsub.s1 FR_Y_lo_2 = FR_G, FR_Y_hi |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // r_cor = r_cor + Y_lo |
| // poly = poly_hi + rsq * poly_lo |
| // |
| { .mfi |
| add GR_Table_Ptr = 0x0, GR_table_base // Constants_exp_64_Arg |
| fadd.s1 FR_r_cor = FR_r_cor, FR_Y_lo |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_rsq, FR_poly_lo, FR_poly |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Load L_hi |
| // Load L_lo |
| // all long before they are needed. |
| // They are used in LOGL_RETURN PATH |
| // |
| // Y_lo = Y_lo + r |
| // poly = rsq * poly + r_cor |
| // |
| { .mfi |
| ldfe FR_L_hi = [GR_Table_Ptr],16 // Load L_hi |
| fadd.s1 FR_Y_lo = FR_Y_lo_2, FR_r |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_rsq, FR_poly, FR_r_cor |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfb |
| ldfe FR_L_lo = [GR_Table_Ptr],16 // Load L_lo |
| fadd.s1 FR_Y_lo = FR_Y_lo, FR_poly |
| br.cond.sptk LOGL_RETURN // Branch to common code |
| } |
| ;; |
| |
| |
| LOGL80_NEAR: |
| // Here if |x-1| < 2^-8 |
| // |
| // Branch LOGL80_NEAR |
| // |
| |
| { .mmf |
| ldfe FR_P_8 = [GR_P_ptr1],16 // Load P_8 |
| ldfe FR_P_4 = [GR_P_ptr2],16 // Load P_4 |
| fmpy.s1 FR_Wsq = FR_W, FR_W |
| } |
| ;; |
| |
| { .mmi |
| ldfe FR_P_7 = [GR_P_ptr1],16 // Load P_7 |
| ldfe FR_P_3 = [GR_P_ptr2],16 // Load P_3 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mmi |
| ldfe FR_P_6 = [GR_P_ptr1],16 // Load P_6 |
| ldfe FR_P_2 = [GR_P_ptr2],16 // Load P_2 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mmi |
| ldfe FR_P_5 = [GR_P_ptr1],16 // Load P_5 |
| ldfe FR_P_1 = [GR_P_ptr2],16 // Load P_1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| getf.exp GR_Delta_Exp = FR_Delta // Get signexp of y-1 for exp calc |
| fmpy.s1 FR_W4 = FR_Wsq, FR_Wsq |
| nop.i 999 |
| } |
| { .mfi |
| add GR_Table_Ptr = 0x0, GR_table_base // Constants_exp_64_Arg |
| fmpy.s1 FR_W3 = FR_Wsq, FR_W |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_half_W = FR_Half, FR_W |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_L_hi = [GR_Table_Ptr],16 |
| fma.s1 FR_poly_lo = FR_W, FR_P_8,FR_P_7 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_W, FR_P_4, FR_P_3 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_L_lo = [GR_Table_Ptr],16 |
| fnma.s1 FR_Y_hi = FR_W, FR_half_W, FR_W |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_6 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_W, FR_poly, FR_P_2 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fsub.s1 FR_Y_lo = FR_W, FR_Y_hi |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_lo = FR_W, FR_poly_lo, FR_P_5 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_W, FR_poly, FR_P_1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fnma.s1 FR_Y_lo = FR_W, FR_half_W, FR_Y_lo |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_poly_lo, FR_W4, FR_poly |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_Y_lo = FR_poly, FR_W3, FR_Y_lo |
| nop.i 999 |
| } |
| ;; |
| |
| |
| LOGL_RETURN: |
| // Common code for completion of both logx paths |
| |
| // |
| // L_hi, L_lo already loaded. |
| // |
| // |
| // kernel_log_80 computed ln(X) |
| // and return logX_hi and logX_lo as results. |
| // PR_pow_Safe set as well. |
| // |
| // |
| // Compute Y * (logX_hi + logX_lo) |
| // P_hi -> X |
| // P_lo -> X_cor |
| // (Manipulate names so that inputs are in |
| // the place kernel_exp expects them) |
| // |
| // This function computes exp( x + x_cor) |
| // Input FR 1: FR_X |
| // Input FR 2: FR_X_cor |
| // Output FR 3: FR_Y_hi |
| // Output FR 4: FR_Y_lo |
| // Output FR 5: FR_Scale |
| // Output PR 1: PR_Safe |
| // |
| // P15 is True |
| // |
| // Load constants used in computing N using right-shift technique |
| { .mlx |
| mov GR_exp_2tom51 = 0xffff-51 |
| movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2 |
| } |
| { .mlx |
| add GR_Special_Exp = -50,GR_exp_bias |
| movl GR_rshf_2to51 = 0x4718000000000000 // 1.10000 2^(63+51) |
| } |
| ;; |
| |
| // |
| // Point to Table of W1s |
| // Point to Table of W2s |
| // |
| { .mmi |
| add GR_W1_ptr = 0x2b0, GR_table_base // Constants_exp_64_W1 |
| add GR_W2_ptr = 0x4b0, GR_table_base // Constants_exp_64_W2 |
| cmp.le p6,p0= GR_Delta_Exp,GR_Special_Exp |
| };; |
| |
| // Form two constants we need |
| // 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 |
| // 1.1000..000 * 2^(63+63-12) to right shift int(N) into the significand |
| |
| { .mfi |
| setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63 |
| nop.f 999 |
| and GR_Delta_Exp=GR_Delta_Exp,GR_exp_mask // Get exponent of y-1 |
| } |
| { .mlx |
| setf.d FR_RSHF_2TO51 = GR_rshf_2to51 // Form const 1.1000 * 2^(63+51) |
| movl GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_X_lo = FR_Input_Y, FR_logx_lo // logx_lo is Y_lo |
| cmp.eq p15, p0= r0, r0 // Set p15, assume safe |
| };; |
| |
| { .mmi |
| setf.exp FR_2TOM51 = GR_exp_2tom51 // Form 2^-51 for scaling float_N |
| setf.d FR_RSHF = GR_rshf // Form right shift const 1.1000 * 2^63 |
| add GR_Table_Ptr1 = 0x50, GR_table_base // Constants_exp_64_P for |
| // EXPL_SMALL path |
| } |
| ;; |
| |
| { .mmi |
| ldfe FR_P_6 = [GR_Table_Ptr1],16 // Load P_6 for EXPL_SMALL path |
| ;; |
| ldfe FR_P_5 = [GR_Table_Ptr1],16 // Load P_5 for EXPL_SMALL path |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_P_4 = [GR_Table_Ptr1],16 // Load P_4 for EXPL_SMALL path |
| fma.s1 FR_P_hi = FR_Input_Y, FR_logx_hi,FR_X_lo // logx_hi ix Y_hi |
| nop.i 999 |
| } |
| ;; |
| |
| { .mmi |
| ldfe FR_P_3 = [GR_Table_Ptr1],16 // Load P_3 for EXPL_SMALL path |
| ;; |
| ldfe FR_P_2 = [GR_Table_Ptr1],16 // Load P_2 for EXPL_SMALL path |
| nop.i 999 |
| } |
| ;; |
| |
| // N = X * Inv_log2_by_2^12 |
| // By adding 1.10...0*2^63 we shift and get round_int(N_signif) in significand. |
| // We actually add 1.10...0*2^51 to X * Inv_log2 to do the same thing. |
| { .mfi |
| ldfe FR_P_1 = [GR_Table_Ptr1] // Load P_1 for EXPL_SMALL path |
| fma.s1 FR_N = FR_X, FR_INV_LN2_2TO63, FR_RSHF_2TO51 |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| fms.s1 FR_P_lo= FR_Input_Y, FR_logx_hi, FR_P_hi // P_hi is X |
| (p6) br.cond.spnt POWL_Y_ALMOST_1 // Branch if |y-1| < 2^-50 |
| } |
| ;; |
| |
| { .mmi |
| getf.exp GR_Expo_X = FR_X |
| add GR_T1_ptr = 0x0b0, GR_table_base // Constants_exp_64_T1 |
| add GR_T2_ptr = 0x1b0, GR_table_base // Constants_exp_64_T2 |
| } |
| ;; |
| |
| // float_N = round_int(N) |
| // The signficand of N contains the rounded integer part of X * 2^12/ln2, |
| // as a twos complement number in the lower bits (that is, it may be negative). |
| // That twos complement number (called N) is put into GR_N_fix. |
| |
| // Since N is scaled by 2^51, it must be multiplied by 2^-51 |
| // before the shift constant 1.10000 * 2^63 is subtracted to yield float_N. |
| // Thus, float_N contains the floating point version of N |
| |
| |
| { .mfi |
| add GR_Table_Ptr = 0x20, GR_table_base // Constants_exp_64_A |
| fms.s1 FR_float_N = FR_N, FR_2TOM51, FR_RSHF // Form float_N |
| nop.i 999 |
| } |
| // Create low part of Y(ln(x)_hi + ln(x)_lo) as P_lo |
| { .mfi |
| mov GR_Big_Pos_Exp = 0x3ffe // 16382, largest safe exponent |
| fadd.s1 FR_P_lo = FR_P_lo, FR_X_lo |
| mov GR_Big_Neg_Exp = -0x3ffd // -16381 smallest safe exponent |
| };; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_rsq = FR_X, FR_X // rsq = X*X for EXPL_SMALL path |
| mov GR_vsm_expo = -70 // Exponent for very small path |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_lo = FR_P_6, FR_X, FR_P_5 // poly_lo for EXPL_SMALL path |
| add GR_temp = 0x1,r0 // For tiny signif if small path |
| } |
| ;; |
| |
| // |
| // If expo_X < -6 goto exp_small |
| // |
| { .mmi |
| getf.sig GR_N_fix = FR_N |
| ldfe FR_A_3 = [GR_Table_Ptr],16 // Load A_3 |
| and GR_Expo_X = GR_Expo_X, GR_exp_mask // Get exponent of X |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_A_2 = [GR_Table_Ptr],16 // Load A_2 |
| nop.f 999 |
| sub GR_Expo_X = GR_Expo_X, GR_exp_bias // Get true exponent of X |
| } |
| ;; |
| |
| // |
| // If -6 > Expo_X, set P9 and branch |
| // |
| { .mfb |
| cmp.gt p9, p0 = -6, GR_Expo_X |
| fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_X // r = X - L_hi * float_N |
| (p9) br.cond.spnt EXPL_SMALL // Branch if |X| < 2^-6 |
| } |
| ;; |
| |
| // |
| // If 14 <= Expo_X, set P10 |
| // |
| { .mib |
| cmp.le p10, p0 = 14, GR_Expo_X |
| nop.i 999 |
| (p10) br.cond.spnt EXPL_HUGE // Branch if |X| >= 2^14 |
| } |
| ;; |
| |
| // |
| // Load single T1 |
| // Load single T2 |
| // W_1_p1 = W_1 + 1 |
| // |
| { .mmi |
| nop.m 999 |
| nop.m 999 |
| extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1 |
| } |
| ;; |
| |
| // |
| // k = extr.u(N_fix,0,6) |
| // |
| { .mmi |
| shladd GR_W1_ptr = GR_M1,3,GR_W1_ptr // Point to W1 |
| shladd GR_T1_ptr = GR_M1,2,GR_T1_ptr // Point to T1 |
| extr.u GR_M2 = GR_N_fix, 0, 6 // Extract index M_2 |
| } |
| ;; |
| |
| // N_fix is only correct up to 50 bits because of our right shift technique. |
| // Actually in the normal path we will have restricted K to about 14 bits. |
| // Somewhat arbitrarily we extract 32 bits. |
| { .mmi |
| ldfd FR_W1 = [GR_W1_ptr] |
| shladd GR_W2_ptr = GR_M2,3,GR_W2_ptr // Point to W2 |
| extr GR_k = GR_N_fix, 12, 32 // Extract k |
| } |
| ;; |
| |
| { .mfi |
| ldfs FR_T1 = [GR_T1_ptr] |
| fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r |
| shladd GR_T2_ptr = GR_M2,2,GR_T2_ptr // Point to T2 |
| } |
| { .mfi |
| add GR_exp_bias_p_k = GR_exp_bias, GR_k |
| nop.f 999 |
| cmp.gt p14,p15 = GR_k,GR_Big_Pos_Exp |
| } |
| ;; |
| |
| // |
| // if k < big_neg_exp, set p14 and Safe=False |
| // |
| { .mmi |
| ldfs FR_T2 = [GR_T2_ptr] |
| (p15) cmp.lt p14,p15 = GR_k,GR_Big_Neg_Exp |
| nop.i 999 |
| } |
| ;; |
| |
| { .mmi |
| setf.exp FR_Scale = GR_exp_bias_p_k |
| ldfd FR_W2 = [GR_W2_ptr] |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| ldfe FR_A_1 = [GR_Table_Ptr],16 |
| fadd.s1 FR_r = FR_r, FR_X_cor |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fadd.s1 FR_W_1_p1 = FR_W1, f1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_r, FR_A_3, FR_A_2 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_rsq = FR_r, FR_r |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_T = FR_T1, FR_T2 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_W = FR_W2, FR_W_1_p1, FR_W1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_TMP1 = FR_Scale, FR_Sgn, f0 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_r, FR_poly, FR_A_1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_TMP2 = FR_T, f1, f0 // TMP2 = Y_hi = T |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fadd.s1 FR_Wp1 = FR_W, f1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly = FR_rsq, FR_poly,FR_r |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_Tscale = FR_T, FR_TMP1, f0 // Scale * Sgn * T |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_Y_lo = FR_Wp1, FR_poly, FR_W |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| fmpy.s1 FR_TMP3 = FR_Y_lo, FR_Tscale |
| br.cond.sptk POWL_64_SHARED |
| } |
| ;; |
| |
| |
| EXPL_SMALL: |
| // Here if |ylogx| < 2^-6 |
| // |
| // Begin creating lsb to perturb final result |
| // |
| { .mfi |
| setf.sig FR_temp = GR_temp |
| fma.s1 FR_poly_lo = FR_poly_lo, FR_X, FR_P_4 |
| cmp.lt p12, p0 = GR_Expo_X, GR_vsm_expo // Test |ylogx| < 2^-70 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_hi = FR_P_2, FR_X, FR_P_1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_TMP2 = f1, f1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_TMP1 = FR_Sgn, f1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_r4 = FR_rsq, FR_rsq |
| (p12) cmp.eq p15, p0 = r0, r0 // Set safe if |ylogx| < 2^-70 |
| } |
| { .mfb |
| nop.m 999 |
| (p12) fmpy.s1 FR_TMP3 = FR_Sgn, FR_X |
| (p12) br.cond.spnt POWL_64_SHARED // Branch if |ylogx| < 2^-70 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_lo = FR_poly_lo, FR_X, FR_P_3 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, FR_X |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s1 FR_Y_lo = FR_poly_lo, FR_r4, FR_poly_hi |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_TMP3 = FR_Y_lo, FR_TMP1 // Add sign info |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Toggle on last bit of Y_lo |
| // Set lsb of Y_lo to 1 |
| // |
| { .mfi |
| nop.m 999 |
| for FR_temp = FR_Y_lo,FR_temp |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| fmerge.se FR_TMP3 = FR_TMP3,FR_temp |
| br.cond.sptk POWL_64_SHARED |
| } |
| ;; |
| |
| |
| EXPL_HUGE: |
| // Here if |ylogx| >= 2^14 |
| { .mfi |
| mov GR_temp = 0x0A1DC // If X < 0, exponent -24100 |
| fcmp.gt.s1 p12, p13 = FR_X, f0 // Test X > 0 |
| cmp.eq p14, p15 = r0, r0 // Set Safe to false |
| } |
| ;; |
| |
| { .mmi |
| (p12) mov GR_Mask = 0x15DC0 // If X > 0, exponent +24000 |
| (p13) mov GR_Mask = 0x0A240 // If X < 0, exponent -24000 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mmf |
| setf.exp FR_TMP2 = GR_Mask // Form Y_hi = TMP2 |
| (p13) setf.exp FR_Y_lo = GR_temp // If X < 0, Y_lo = 2^-24100 |
| (p12) mov FR_Y_lo = f1 // IF X > 0, Y_lo = 1.0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fmpy.s1 FR_TMP1 = FR_TMP2, FR_Sgn // TMP1 = Y_hi * Sgn |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| fmpy.s1 FR_TMP3 = FR_Y_lo,FR_TMP1 // TMP3 = Y_lo * (Y_hi * Sgn) |
| br.cond.sptk POWL_64_SHARED |
| } |
| ;; |
| |
| POWL_Y_ALMOST_1: |
| // Here if delta = |y-1| < 2^-50 |
| // |
| // x**(1 + delta) = x * e (ln(x)*delta) = x ( 1 + ln(x) * delta) |
| // |
| // Computation will be safe for 2^-16381 <= x < 2^16383 |
| |
| { .mfi |
| mov GR_exp_ynear1_oflow = 0xffff + 16383 |
| fma.s1 FR_TMP1 = FR_Input_X,FR_Delta,f0 |
| and GR_exp_x = GR_exp_mask, GR_signexp_x |
| } |
| ;; |
| |
| { .mfi |
| cmp.lt p15, p14 = GR_exp_x, GR_exp_ynear1_oflow |
| fma.s1 FR_TMP2 = FR_logx_hi,f1,FR_X_lo |
| mov GR_exp_ynear1_uflow = 0xffff - 16381 |
| } |
| ;; |
| |
| { .mfb |
| (p15) cmp.ge p15, p14 = GR_exp_x, GR_exp_ynear1_uflow |
| fma.s1 FR_TMP3 = FR_Input_X,f1,f0 |
| br.cond.sptk POWL_64_SHARED |
| };; |
| |
| POWL_64_SQUARE: |
| // |
| // Here if x not zero and y=2. |
| // |
| // Setup for multipath code |
| // |
| { .mfi |
| mov GR_exp_square_oflow = 0xffff + 8192 // Exponent where x*x overflows |
| fmerge.se FR_TMP1 = FR_Input_X, FR_Input_X |
| and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x |
| } |
| ;; |
| |
| { .mfi |
| cmp.lt p15, p14 = GR_exp_x, GR_exp_square_oflow // Decide safe/unsafe |
| fmerge.se FR_TMP2 = FR_Input_X, FR_Input_X |
| mov GR_exp_square_uflow = 0xffff - 8191 // Exponent where x*x underflows |
| } |
| ;; |
| |
| { .mfi |
| (p15) cmp.ge p15, p14 = GR_exp_x, GR_exp_square_uflow // Decide safe/unsafe |
| fma.s1 FR_TMP3 = f0,f0,f0 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // This is the shared path that will set overflow and underflow. |
| // |
| POWL_64_SHARED: |
| |
| // |
| // Return if no danger of over or underflow. |
| // |
| { .mfb |
| nop.m 999 |
| fma.s0 FR_Result = FR_TMP1, FR_TMP2, FR_TMP3 |
| (p15) br.ret.sptk b0 // Main path return if certain no over/underflow |
| } |
| ;; |
| |
| // |
| // S0 user supplied status |
| // S2 user supplied status + WRE + TD (Overflows) |
| // S2 user supplied status + FZ + TD (Underflows) |
| // |
| // |
| // If (Safe) is true, then |
| // Compute result using user supplied status field. |
| // No overflow or underflow here, but perhaps inexact. |
| // Return |
| // Else |
| // Determine if overflow or underflow was raised. |
| // Fetch +/- overflow threshold for IEEE double extended |
| |
| { .mfi |
| nop.m 999 |
| fsetc.s2 0x7F,0x41 // For underflow test, set S2=User+TD+FTZ |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s2 FR_Result_small = FR_TMP1, FR_TMP2, FR_TMP3 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fsetc.s2 0x7F,0x42 // For overflow test, set S2=User+TD+WRE |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fma.s2 FR_Result_big = FR_TMP1, FR_TMP2,FR_TMP3 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fsetc.s2 0x7F,0x40 // Reset S2=User |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p11, p0 = FR_Result_small, 0x00F // Test small result unorm/zero |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fcmp.ge.s1 p8, p0 = FR_Result_big , FR_Big // Test >= + oflow threshold |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfb |
| (p11) mov GR_Parameter_TAG = 19 // Set tag for underflow |
| fcmp.le.s1 p9, p0 = FR_Result_big, FR_NBig // Test <= - oflow threshold |
| (p11) br.cond.spnt __libm_error_region // Branch if pow underflowed |
| } |
| ;; |
| |
| { .mfb |
| (p8) mov GR_Parameter_TAG = 18 // Set tag for overflow |
| nop.f 999 |
| (p8) br.cond.spnt __libm_error_region // Branch if pow +overflow |
| } |
| ;; |
| |
| { .mbb |
| (p9) mov GR_Parameter_TAG = 18 // Set tag for overflow |
| (p9) br.cond.spnt __libm_error_region // Branch if pow -overflow |
| br.ret.sptk b0 // Branch if result really ok |
| } |
| ;; |
| |
| |
| POWL_64_SPECIAL: |
| // Here if x or y is NatVal, nan, inf, or zero |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s1 p15, p0 = FR_Input_X, f1 // Test x=+1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p8, p0 = FR_Input_X, 0x143 // Test x natval, snan |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p15) fcmp.eq.unc.s0 p6,p0 = FR_Input_Y, f0 // If x=1, flag invalid if y=SNaN |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p15) fmpy.s0 FR_Result = f1,f1 // If x=1, result=1 |
| (p15) br.ret.spnt b0 // Exit if x=1 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p6, p0 = FR_Input_Y, 0x007 // Test y zero |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p9, p0 = FR_Input_Y, 0x143 // Test y natval, snan |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p10, p0 = FR_Input_X, 0x083 // Test x qnan |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p8) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X // If x=snan, result=qnan |
| (p6) cmp.ne p8,p0 = r0,r0 // Don't exit if x=snan, y=0 ==> result=+1 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p6) fclass.m.unc p15, p0 = FR_Input_X,0x007 // Test x=0, y=0 |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p9) fmpy.s0 FR_Result = FR_Input_Y, FR_Input_X // If y=snan, result=qnan |
| (p8) br.ret.spnt b0 // Exit if x=snan, y not 0, |
| // result=qnan |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s1 p7, p0 = FR_Input_Y, f1 // Test y +1.0 |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p10) fmpy.s0 FR_Result = FR_Input_X, f0 // If x=qnan, result=qnan |
| (p9) br.ret.spnt b0 // Exit if y=snan, result=qnan |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p6) fclass.m.unc p8, p0 = FR_Input_X,0x0C3 // Test x=nan, y=0 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p6) fcmp.eq.s0 p9,p0 = FR_Input_X, f0 // If y=0, flag if x denormal |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p6) fadd.s0 FR_Result = f1, f0 // If y=0, result=1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p11, p0 = FR_Input_Y, 0x083 // Test y qnan |
| nop.i 999 |
| } |
| { .mfb |
| (p15) mov GR_Parameter_TAG = 20 // Error tag for x=0, y=0 |
| (p7) fmpy.s0 FR_Result = FR_Input_X,f1 // If y=1, result=x |
| (p15) br.cond.spnt __libm_error_region // Branch if x=0, y=0, result=1 |
| } |
| ;; |
| |
| { .mfb |
| (p8) mov GR_Parameter_TAG = 23 // Error tag for x=nan, y=0 |
| fclass.m p14, p0 = FR_Input_Y, 0x023 // Test y inf |
| (p8) br.cond.spnt __libm_error_region // Branch if x=snan, y=0, |
| // result=1 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| fclass.m p13, p0 = FR_Input_X, 0x023 // Test x inf |
| (p6) br.ret.spnt b0 // Exit y=0, x not nan or 0, |
| // result=1 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| (p14) fcmp.eq.unc.s1 p0,p14 = FR_Input_X,f0 // Test x not 0, y=inf |
| (p7) br.ret.spnt b0 // Exit y=1, x not snan, |
| // result=x |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| (p10) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X // If x=qnan, y not snan, |
| // result=qnan |
| (p10) br.ret.spnt b0 // Exit x=qnan, y not snan, |
| // result=qnan |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| (p11) fmpy.s0 FR_Result = FR_Input_Y,FR_Input_X // If y=qnan, x not nan or 1, |
| // result=qnan |
| (p11) br.ret.spnt b0 // Exit y=qnan, x not nan or 1, |
| // result=qnan |
| } |
| ;; |
| |
| { .mbb |
| nop.m 999 |
| (p14) br.cond.spnt POWL_64_Y_IS_INF // Branch if y=inf, x not 1 or nan |
| (p13) br.cond.spnt POWL_64_X_IS_INF // Branch if x=inf, y not 1 or nan |
| } |
| ;; |
| |
| |
| POWL_64_X_IS_ZERO: |
| // Here if x=0, y not nan or 1 or inf or 0 |
| |
| // There is logic starting here to determine if y is an integer when x = 0. |
| // If 0 < |y| < 1 then clearly y is not an integer. |
| // If |y| > 1, then the significand of y is shifted left by the size of |
| // the exponent of y. This preserves the lsb of the integer part + the |
| // fractional bits. The lsb of the integer can be tested to determine if |
| // the integer is even or odd. The fractional bits can be tested. If zero, |
| // then y is an integer. |
| // |
| { .mfi |
| and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent of y |
| nop.f 999 |
| and GR_y_sign = GR_sign_mask,GR_signexp_y // Get sign of y |
| } |
| ;; |
| |
| // |
| // Maybe y is < 1 already, so |
| // can never be an integer. |
| // |
| { .mfi |
| cmp.lt p9, p8 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 |
| nop.f 999 |
| sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent of y |
| } |
| ;; |
| |
| // |
| // Shift significand of y looking for nonzero bits |
| // For y > 1, shift signif_y exp_y bits to the left |
| // For y < 1, turn on 4 low order bits of significand of y |
| // so that the fraction will always be non-zero |
| // |
| { .mmi |
| (p9) or GR_exp_y= 0xF,GR_signif_y // Force nonzero fraction if y<1 |
| ;; |
| nop.m 999 |
| (p8) shl GR_exp_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction |
| // Wait 4 cycles to use result |
| } |
| ;; |
| |
| { .mmi |
| nop.m 999 |
| ;; |
| nop.m 999 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mmi |
| nop.m 999 |
| ;; |
| nop.m 999 |
| shl GR_fraction_y= GR_exp_y,1 // Shift left 1 to get fraction |
| } |
| ;; |
| |
| // |
| // Integer part of y shifted off. |
| // Get y's low even or odd bit - y might not be an int. |
| // |
| { .mii |
| cmp.eq p13,p0 = GR_fraction_y, r0 // Test for y integer |
| cmp.eq p8,p0 = GR_y_sign, r0 // Test for y > 0 |
| ;; |
| (p13) tbit.nz.unc p13,p0 = GR_exp_y, 63 // Test if y an odd integer |
| } |
| ;; |
| |
| { .mfi |
| (p13) cmp.eq.unc p13,p14 = GR_y_sign, r0 // Test y pos odd integer |
| (p8) fcmp.eq.s0 p12,p0 = FR_Input_Y, f0 // If x=0 and y>0 flag if y denormal |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Return +/-0 when x=+/-0 and y is positive odd integer |
| // |
| { .mfb |
| nop.m 999 |
| (p13) mov FR_Result = FR_Input_X // If x=0, y pos odd int, result=x |
| (p13) br.ret.spnt b0 // Exit x=0, y pos odd int, result=x |
| } |
| ;; |
| |
| // |
| // Return +/-inf when x=+/-0 and y is negative odd int |
| // |
| { .mfb |
| (p14) mov GR_Parameter_TAG = 21 |
| (p14) frcpa.s0 FR_Result, p0 = f1, FR_Input_X // Result +-inf, set Z flag |
| (p14) br.cond.spnt __libm_error_region |
| } |
| ;; |
| |
| // |
| // Return +0 when x=+/-0 and y positive and not an odd integer |
| // |
| { .mfb |
| nop.m 999 |
| (p8) mov FR_Result = f0 // If x=0, y>0 and not odd integer, result=+0 |
| (p8) br.ret.sptk b0 // Exit x=0, y>0 and not odd integer, result=+0 |
| } |
| ;; |
| |
| // |
| // Return +inf when x=+/-0 and y is negative and not odd int |
| // |
| { .mfb |
| mov GR_Parameter_TAG = 21 |
| frcpa.s0 FR_Result, p10 = f1,f0 // Result +inf, raise Z flag |
| br.cond.sptk __libm_error_region |
| } |
| ;; |
| |
| |
| POWL_64_X_IS_INF: |
| // |
| // Here if x=inf, y not 1 or nan |
| // |
| { .mfi |
| and GR_exp_y = GR_exp_mask,GR_signexp_y // Get biased exponent y |
| fclass.m p13, p0 = FR_Input_X,0x022 // Test x=-inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| and GR_y_sign = GR_sign_mask,GR_signexp_y // Get sign of y |
| fcmp.eq.s0 p9,p0 = FR_Input_Y, f0 // Dummy to set flag if y denorm |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Maybe y is < 1 already, so |
| // isn't an int. |
| // |
| { .mfi |
| (p13) cmp.lt.unc p9, p8 = GR_exp_y,GR_exp_bias // Test 0 < |y| < 1 if x=-inf |
| fclass.m p11, p0 = FR_Input_X,0x021 // Test x=+inf |
| sub GR_exp_y = GR_exp_y,GR_exp_bias // Get true exponent y |
| } |
| ;; |
| |
| // |
| // Shift significand of y looking for nonzero bits |
| // For y > 1, shift signif_y exp_y bits to the left |
| // For y < 1, turn on 4 low order bits of significand of y |
| // so that the fraction will always be non-zero |
| // |
| { .mmi |
| (p9) or GR_exp_y= 0xF,GR_signif_y // Force nonzero fraction if y<1 |
| ;; |
| (p11) cmp.eq.unc p14,p12 = GR_y_sign, r0 // Test x=+inf, y>0 |
| (p8) shl GR_exp_y= GR_signif_y,GR_exp_y // Get lsb of int + fraction |
| // Wait 4 cycles to use result |
| } |
| ;; |
| |
| // |
| // Return +inf for x=+inf, y > 0 |
| // Return +0 for x=+inf, y < 0 |
| // |
| { .mfi |
| nop.m 999 |
| (p12) mov FR_Result = f0 // If x=+inf, y<0, result=+0 |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p14) fma.s0 FR_Result = FR_Input_X,f1,f0 // If x=+inf, y>0, result=+inf |
| (p11) br.ret.sptk b0 // Exit x=+inf |
| } |
| ;; |
| |
| // |
| // Here only if x=-inf. Wait until can use result of shl... |
| // |
| { .mmi |
| nop.m 999 |
| ;; |
| nop.m 999 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| cmp.eq p8,p9 = GR_y_sign, r0 // Test y pos |
| nop.f 999 |
| shl GR_fraction_y = GR_exp_y,1 // Shift left 1 to get fraction |
| } |
| ;; |
| |
| { .mmi |
| cmp.eq p13,p0 = GR_fraction_y, r0 // Test y integer |
| ;; |
| nop.m 999 |
| (p13) tbit.nz.unc p13,p0 = GR_exp_y, 63 // Test y odd integer |
| } |
| ;; |
| |
| // |
| // Is y even or odd? |
| // |
| { .mii |
| (p13) cmp.eq.unc p14,p10 = GR_y_sign, r0 // Test x=-inf, y pos odd int |
| (p13) cmp.ne.and p8,p9 = r0,r0 // If y odd int, turn off p8,p9 |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Return -0 for x = -inf and y < 0 and odd int. |
| // Return -Inf for x = -inf and y > 0 and odd int. |
| // |
| { .mfi |
| nop.m 999 |
| (p10) fmerge.ns FR_Result = f0, f0 // If x=-inf, y neg odd int, result=-0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p14) fmpy.s0 FR_Result = FR_Input_X,f1 // If x=-inf, y pos odd int, result=-inf |
| nop.i 999 |
| } |
| ;; |
| |
| // |
| // Return Inf for x = -inf and y > 0 not an odd int. |
| // Return +0 for x = -inf and y < 0 not an odd int. |
| // |
| .pred.rel "mutex",p8,p9 |
| { .mfi |
| nop.m 999 |
| (p8) fmerge.ns FR_Result = FR_Input_X, FR_Input_X // If x=-inf, y>0 not odd int |
| // result=+inf |
| nop.i 999 |
| } |
| { .mfb |
| nop.m 999 |
| (p9) fmpy.s0 FR_Result = f0,f0 // If x=-inf, y<0 not odd int |
| // result=+0 |
| br.ret.sptk b0 // Exit for x=-inf |
| } |
| ;; |
| |
| |
| POWL_64_Y_IS_INF: |
| // Here if y=inf, x not 1 or nan |
| // |
| // For y = +Inf and |x| < 1 returns 0 |
| // For y = +Inf and |x| > 1 returns Inf |
| // For y = -Inf and |x| < 1 returns Inf |
| // For y = -Inf and |x| > 1 returns 0 |
| // For y = Inf and |x| = 1 returns 1 |
| // |
| { .mfi |
| nop.m 999 |
| fclass.m p8, p0 = FR_Input_Y, 0x021 // Test y=+inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fclass.m p9, p0 = FR_Input_Y, 0x022 // Test y=-inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fabs FR_X = FR_Input_X // Form |x| |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s0 p10,p0 = FR_Input_X, f0 // flag if x denormal |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p8) fcmp.lt.unc.s1 p6, p0 = FR_X, f1 // Test y=+inf, |x|<1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p8) fcmp.gt.unc.s1 p7, p0 = FR_X, f1 // Test y=+inf, |x|>1 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p9) fcmp.lt.unc.s1 p12, p0 = FR_X, f1 // Test y=-inf, |x|<1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p6) fmpy.s0 FR_Result = f0,f0 // If y=+inf, |x|<1, result=+0 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p9) fcmp.gt.unc.s1 p13, p0 = FR_X, f1 // Test y=-inf, |x|>1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p7) fmpy.s0 FR_Result = FR_Input_Y, f1 // If y=+inf, |x|>1, result=+inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| fcmp.eq.s1 p14, p0 = FR_X, f1 // Test y=inf, |x|=1 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p12) fnma.s0 FR_Result = FR_Input_Y, f1, f0 // If y=-inf, |x|<1, result=+inf |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 999 |
| (p13) mov FR_Result = f0 // If y=-inf, |x|>1, result=+0 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 999 |
| (p14) fmpy.s0 FR_Result = f1,f1 // If y=inf, |x|=1, result=+1 |
| br.ret.sptk b0 // Common return for y=inf |
| } |
| ;; |
| |
| |
| // Here if x or y denorm/unorm |
| POWL_DENORM: |
| { .mmi |
| getf.sig GR_signif_Z = FR_norm_X // Get significand of x |
| ;; |
| getf.exp GR_signexp_y = FR_norm_Y // Get sign and exp of y |
| nop.i 999 |
| } |
| ;; |
| |
| { .mfi |
| getf.sig GR_signif_y = FR_norm_Y // Get significand of y |
| nop.f 999 |
| nop.i 999 |
| } |
| ;; |
| |
| { .mib |
| getf.exp GR_signexp_x = FR_norm_X // Get sign and exp of x |
| extr.u GR_Index1 = GR_signif_Z, 59, 4 // Extract upper 4 signif bits of x |
| br.cond.sptk POWL_COMMON // Branch back to main path |
| } |
| ;; |
| |
| |
| POWL_64_UNSUPPORT: |
| // |
| // Raise exceptions for specific |
| // values - pseudo NaN and |
| // infinities. |
| // Return NaN and raise invalid |
| // |
| { .mfb |
| nop.m 999 |
| fmpy.s0 FR_Result = FR_Input_X,f0 |
| br.ret.sptk b0 |
| } |
| ;; |
| |
| POWL_64_XNEG: |
| // |
| // Raise invalid for x < 0 and |
| // y not an integer |
| // |
| { .mfi |
| nop.m 999 |
| frcpa.s0 FR_Result, p8 = f0, f0 |
| mov GR_Parameter_TAG = 22 |
| } |
| { .mib |
| nop.m 999 |
| nop.i 999 |
| br.cond.sptk __libm_error_region |
| } |
| ;; |
| |
| POWL_64_SQRT: |
| { .mfi |
| nop.m 999 |
| frsqrta.s0 FR_Result,p10 = FR_save_Input_X |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f62=FR_Half,FR_save_Input_X,f0 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f63=FR_Result,FR_Result,f0 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fnma.s1 f32=f63,f62,FR_Half |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f33=f32,FR_Result,FR_Result |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f34=f33,f62,f0 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fnma.s1 f35=f34,f33,FR_Half |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f63=f35,f33,f33 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f32=FR_save_Input_X,f63,f0 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 FR_Result=f63,f62,f0 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f33=f11,f63,f0 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fnma.s1 f34=f32,f32,FR_save_Input_X |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fnma.s1 f35=FR_Result,f63,FR_Half |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f62=f33,f34,f32 |
| nop.i 999 |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fma.s1 f63=f33,f35,f33 |
| nop.i 999 ;; |
| } |
| { .mfi |
| nop.m 999 |
| (p10) fnma.s1 f32=f62,f62,FR_save_Input_X |
| nop.i 999 ;; |
| } |
| { .mfb |
| nop.m 999 |
| (p10) fma.s0 FR_Result=f32,f63,f62 |
| br.ret.sptk b0 // Exit for x > 0, y = 0.5 |
| } |
| ;; |
| |
| GLOBAL_LIBM_END(powl) |
| |
| |
| LOCAL_LIBM_ENTRY(__libm_error_region) |
| .prologue |
| { .mfi |
| add GR_Parameter_Y=-32,sp // Parameter 2 value |
| nop.f 0 |
| .save ar.pfs,GR_SAVE_PFS |
| mov GR_SAVE_PFS=ar.pfs // Save ar.pfs |
| } |
| { .mfi |
| .fframe 64 |
| add sp=-64,sp // Create new stack |
| nop.f 0 |
| mov GR_SAVE_GP=gp // Save gp |
| };; |
| { .mmi |
| stfe [GR_Parameter_Y] = FR_Input_Y,16 // Save Parameter 2 on stack |
| add GR_Parameter_X = 16,sp // Parameter 1 address |
| .save b0, GR_SAVE_B0 |
| mov GR_SAVE_B0=b0 // Save b0 |
| };; |
| .body |
| { .mib |
| stfe [GR_Parameter_X] = FR_save_Input_X // Store Parameter 1 on stack |
| add GR_Parameter_RESULT = 0,GR_Parameter_Y |
| nop.b 0 // Parameter 3 address |
| } |
| { .mib |
| stfe [GR_Parameter_Y] = FR_Result // Store Parameter 3 on stack |
| add GR_Parameter_Y = -16,GR_Parameter_Y |
| br.call.sptk b0=__libm_error_support# // Call error handling function |
| };; |
| { .mmi |
| add GR_Parameter_RESULT = 48,sp |
| nop.m 0 |
| nop.i 0 |
| };; |
| { .mmi |
| ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack |
| .restore sp |
| add sp = 64,sp // Restore stack pointer |
| mov b0 = GR_SAVE_B0 // Restore return address |
| };; |
| { .mib |
| mov gp = GR_SAVE_GP // Restore gp |
| mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs |
| br.ret.sptk b0 // Return |
| };; |
| |
| LOCAL_LIBM_END(__libm_error_region#) |
| .type __libm_error_support#,@function |
| .global __libm_error_support# |
